Radiation therapy is used to treat malignant tissue, such as cancer cells. The radiation can have an electromagnetic form, such as high-energy photons, or a particulate form, such as an electron, proton, neutron, or alpha particles.
Fast and accurate dose determination is important for radiation therapy treatment planning to ensure that the correct dose is delivered to a specific patient. Dose determination generally includes two parts: a source model and a transport model. The source model provides the incident fluence, which is the flux of the radiation integrated over time. The transport model determines the dose that results from the incident fluence. In conventional treatment planning system the transport model is a performance bottleneck. The three main transport methods in an order of increasing accuracy or decreasing performance are pencil beam, superposition and convolution, and Monte Carlo simulation. Superposition and convolution is the most common method for determining the radiation dose for external beam radiation therapy.
In particle beam radiation therapy treatment, a tissue volume is irradiated by a large number of directed pencil beams of radiation at various depths. Typically, the treatment planning volume, which represents a region within the patient, is partitioned into a rectangular 3D grid of voxels. To validate a treatment plan, it is necessary to determine the irradiation pattern of tens of thousands of beams for millions of voxels in the volume. To optimize a dose plan, it is necessary to determine the adjoint of this operation.
The radiation pattern can be modeled as a spatial distribution of radiation deposited by each beam. The relative intensity of radiation delivered to the ith voxel by the jth beam is represented by a positive number Aij and the table of numbers for all such beams and voxels is called a fluence matrix AεRV×P, wherein V is a number of voxels and P is a number of pencil beams. In present-day treatment settings there may be V≧106 voxels and P≈105 pencil beams, resulting in a fluence matrix of 8V P≈1012 bytes. This is too large to be stored in conventional memories, or used even in most supercomputers. Thus, the direct determination of the fluence matrix A is currently impractical.
Some dose calculation methods determine a cumulative voxel radiation dose applied during the treatment without explicitly constructing the fluence matrix. Some conventional methods determine the cumulative voxel radiation dose via Monte Carlo simulation or via clinically validated approximations. For example, one method calculate the contributions of the pencil-beams one at a time, e.g., by ray-tracing 3D dose distribution each pencil beam, and accumulate the result into a 3D array representing the cumulative doses to all voxels, see U.S. Pat. No. 8,325,878.
Some state-of-the-art dose optimization techniques use a sparse approximation of the fluence matrix, in which a subset of fluence values above a predetermined threshold are stored, and the remaining small fluence values are neglected. However, such a sparse enough matrix that can be stored in a computer memory disregards about 1-4% of the total radiation.
In addition, the conventional methods are not fast enough for a real time dose calculation. Further, those methods are not suitable to determine the action of the adjoint AT of the fluence matrix, which can be necessary to determine the gradient of the error in various dose optimization techniques.